论文标题
Sitnikov型溶液，用于在BIER4BP中进行无穷小质量运动
Sitnikov-type solution for the motion of infinitesimal mass in BiER4BP
论文作者
论文摘要
在本文中，我们提出了一个新的ANSATZ，用于在四个身体的双elliptic限制问题（BIER4BP）（BIER4BP）（其中三个PRIMORIES M1，M1，M2，M3围绕其共同的质量上椭圆形轨道旋转具有层次构造的层次结构构造M3 <m3 <m1）的新的ANSATZ。这里实施了一种新型的求解程序，以获得无穷小质量m的坐标。同时，就半分析（近似）的方式而言，运动方程式已成功探索了溶液的呈现。我们获得如下：1）坐标{x，y} = {0，0}的解决方案在考虑{m3，m2} << m1，2）坐标z（f）的表达式上大致满足运动的第一个和第二个方程，并通过2-nd顺序给出了2-nd顺序的表达式，该方程是由2-nd orde sitn sittnikov-tore sitnikov-tope yimed siternikov-typepe typepepepepepepepepepepepepepe。这意味着测试粒子正在沿Z轴移动，向外移动系统的常见barycenter（但垂直于所有初选的相互旋转的平面）。
In this paper, we present a new ansatz for approximated solving equations of motion of the infinitesimal mass m in case of bi-elliptic restricted problem of four bodies (BiER4BP) (where three primaries M1, M2, M3 are rotating around their common centre of mass on elliptic orbits with hierarchical configuration M3 < M2 << M1). A new type of the solving procedure is implemented here to obtain the coordinates of the infinitesimal mass m. Meanwhile, the system of equations of motion has been successfully explored with respect to the existence of semi-analytical (approximated) way for presentation of the solution. We obtain as follows: 1) the solution for coordinates {x, y} = {0, 0} is approximately satisfied both the first and second equations of motion if we take into consideration assumption {M3, M2} << M1, 2) the expression for coordinate z(f) is given by the equation of 2-nd order, which describes Sitnikov-type approximated solution. It means that test particle is moving along the z-axis, outward the common barycenter of the system (but perpendicular to the plane of the mutual rotation of all the primaries).
